A method for selecting data points from a finite set of curve points is discussed. The given curve points originate from a smooth curve and are weighted with respect to a local curvature measure. The most significant points are selected and used to approximate the curve. The selected subset of data points is distributed in such a way that they are uniformly distributed with respect to integrated absolute curvature. The technique is tested for various planar curves and is applied to 2D image compression and volume visualization.